Substitute each of the letters by a different decimal digit from 0 to 9 to satisfy this alphametic
square root extraction problem. None of O and P can be 0.
P I E R

√ O P E R A T O R 
C T

B E R
B A C

E P A T
T I A I

P I E O R
P I E O R

Note: Try to derive a non computer assisted method, although computer program/spreadsheet solutions are welcome.
A computer program that considers only whether PIER^2 = OPERATOR yields:
4975 24750625
5061 25613721
but the second one is ruled out as P*P would be OP, rather than the different CT shown.
OPERATOR is therefore 24750625, while
PIER is 4975.
And C is 1 and B is 2416 = 8.
Thus, one need not know the entire squareroot algorithm.
DEFDBL AZ
FOR p = 1 TO 9
IF had(p) = 0 THEN
had(p) = 1
FOR o = 1 TO 9
IF had(o) = 0 THEN
had(o) = 1
FOR i = 0 TO 9
IF had(i) = 0 THEN
had(i) = 1
FOR e = 1 TO 9
IF had(e) = 0 THEN
had(e) = 1
FOR r = 0 TO 9
IF had(r) = 0 THEN
had(r) = 1
FOR a = 0 TO 9
IF had(a) = 0 THEN
had(a) = 1
FOR t = 1 TO 9
IF had(t) = 0 THEN
had(t) = 1
pier = p * 1000 + i * 100 + e * 10 + r
operator = o * 10000010 + p * 1000000 + e * 100000 + r * 10001 + a * 1000 + t * 100
IF pier * pier = operator THEN PRINT pier, operator
had(t) = 0
END IF
NEXT
had(a) = 0
END IF
NEXT
had(r) = 0
END IF
NEXT
had(e) = 0
END IF
NEXT
had(i) = 0
END IF
NEXT
had(o) = 0
END IF
NEXT
had(p) = 0
END IF
NEXT
Note the program considers that E and T are also nonzero in keeping with the spirit of such things, though the same two possibilities are supplied even if zero is allowed for these two variables.

Posted by Charlie
on 20081213 19:24:34 